Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = _ - 3, 6 + 6 = _.

Hook & Objective

5 minutes

In first grade, the operations standards specifically focus on students being able to solve problems where the start is missing. This is the most difficult kind of subtraction problem that students in first grade encounter because it is so difficult to act out! Students can't get a fixed quantity and then directly model it. Using storyboards to think about what happened first, next and last helps kids to conceptually visualize the problems.

Hook: I have some cookies behind my screen. It is a mystery how many I have! You are going to use your smart math brains to figure it out today.

Review and Connect:

We created storyboards for some fun problems yesterday and thought about which part we didn’t know in the story problem. Today, we are going to act out some more story problems. This is important because mathematicians have to be able to solve for every kind of problem, even when they don't know how many to begin with!

Objective:

Your thinking job is: How can I act out and write a matching number sentence for a problem when the whole is missing?

Opening Discussion

Teacher needs a screen or a jar to "hide" the cookies in! Kids can't see how many cookies to begin with.

Present Problem: I have some cookies back here. And I look around the rug and I see _______ doing a great job! So I am going to give her 1 cookie. I have 11 cookies left behind my screen. (I'll show the rest of the cookies). How many cookies did I start with?

Discuss the problem:

Partner talk: What happened first, next and last in the story?

I'll show a chart paper storyboard, students retell the story and the I'll chart what happened.

Which part do we not know? What happened at that part of the story? (The teacher had some cookies and we don’t know how many were behind the screen)

I am going to put a question mark for that part of the story. I don’t know how many cookies I had then so I will put “? Cookies at first”.

Partner talk: What number sentence can we write to match this story?

High level thinking!! Make a prediction: Will the number that goes in this blank be greater or lesser? Why?

Solve the problem: I will give students whiteboards or have them do this at their desk. I want them to quickly show a strategy for how many I started with. Watch this Student Whiteboard Strategies video - you'll see how I structure this time logistically and also a variety of strategies students might use to solve this problem!

After students solve, I'll have students share in partners how they solved and I'll have one student share with the class.

A common misconception you might encounter is students will know the answer, but write an untrue number sentence. Watch a video of one of my students who wrote 11-1=12 on his whiteboard. You'll hear what questions I ask to help him realize his own mistake.

Partner talk: Why was the number at the beginning greater?

11-1=12?

Student Whiteboard Strategies

Student Work Time & Share

15 minutes

Present Student Share Problem: Ms. Cole has cookies in her basket. She gives 2 of them to her friend. She has 13 cookies left. How many cookies did Ms. Cole have in her basket at first?

Students storyboard this problem on whiteboards to push active engagement and then share with a partner. See how one student represented the problem: Student Representation Example

“Now write a number sentence that matches this story. Did we add or take away? We took away! Let’s use a heart for the missing part today”

Partner talk: Check your partner’s storyboard. Does it look like your’s? Are your number sentences the same?

Partner talk Questions:

Will the number that goes in the blank be greater or lesser? Why?

How we can we figure out how many cookies we started with? Some students might need cubes at this point to act it out.

Why did you put the numbers together?

I'll quickly model how 2 students solved, first with cubes to help students visualize the action and then with a number line. This helps students move from concrete (cubes) to a more abstract way of thinking (numerical representation), which supports students engaging with MP2 - Reason abstractly and quantitatively.

Partner talk: Retell that strategy to a partner.

If time, we will do another problem together with whiteboards.

Student Representation Example

Independent Practice

15 minutes

Students storyboard and solve storyboards at their desk! See attached Start Unknown Strategy Guide.docx for ways students might solve. The guide includes different questions you can ask to push students to try more efficient strategies.

Group A: Intervention: Students have numbers under 10

Group B: Right on Track: Students solve problems with numbers under 20

Closing

10 minutes

I'll share one student's strategy to the class. I'll choose a student who used a "Think Addition" strategy. This student combined the two original numbers and either counted on using fingers to keep track or counted on using a number line. This is the next level strategy for most students so I want them to end the day focusing on this idea.